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Abstract
Detecting structures below a cover film at the nanoscale resolution is of essential importance. In this work, we explored factors affecting subsurface material contrast and structural visibility in scattering-type scanning near-field optical microscopy (s-SNOM). A kind of multilayered reference samples containing different buried structures was fabricated and applied for s-SNOM imaging. The dependence of near-field optical contrast on structure geometry, dimension and cover thickness was investigated. Results demonstrate that distinguishing the buried slit pattern is easier than the circular hole with the same critical dimension. The s-SNOM can sense material difference under a more than 100 nm thick polymethyl methacrylate layer and it has a subsurface spatial resolution better than 100 nm.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Micro- and nanoscale devices, such as wearable flexible sensors, integrated circuits and optical metasurfaces, have developed rapidly in recent years [1,2]. Their composed structures are getting more and more complex, which are usually in a three-dimensional or multilayered architecture with the critical dimension reaching nanometer scale. For example, many devices have a thin protective layer to shield electromagnetic interference and improve wear resistance [3]. Owing to various processes involved in fabrication, defects will frequently emerge and have significant influence on the functional performances. To optimize the processing procedures and enhance the yield in massive productions, the non-destructive diagnosis of a complex nano-device is of crucial importance and leads to a great challenge. Though electron microscopy including scanning electron microscopy (SEM) can provide high-resolution topography images, it may be difficult to offer optical or other physical information and thus cannot meet all the inspection demands. Owing to the versatile characterization ability, advanced scanning probe microscopy is another powerful complementary method.
Scattering-type scanning near-field optical microscopy (s-SNOM) is a promising technique for characterizing sample topography and optical properties [4–7]. In contrast to early SNOM instrumentation based on an aperture probe tip for near-field light collection or illumination [8], a metal-coated atomic force microscopy (AFM) tip is used in an s-SNOM system and it behaves like an optical antenna, which tightly confines the incident light into a localized near-field hot spot near the apex [9]. Therefore, s-SNOM overcomes the diffraction limit that restricts the resolution of a conventional optical microscope. The s-SNOM resolution is no longer limited by the light wavelength but mainly related to the tip radius. Nowadays, s-SNOM has been widely used with applications ranging from high-resolution imaging of surfaces to high-sensitivity identification of different materials [10,11]. Furthermore, s-SNOM becomes a powerful tool for field mapping, such as local strain [12–14], carrier concentration [15] and surface polarized phonon [16–18]. In addition to characterization, s-SNOM can serve as a photolithography platform for fabricating patterns at the nanometer scale. Even the probe tip is mainly sensitive to surface or near surface interactions, some studies reported clear optical contrast raising from subsurface materials [19,20]. s-SNOM was proved able to detect 100 nm diameter Au disks covered by a thin SiO2 layer and the influence of tapping amplitude was paid into attention [21]. The imaging of nanostructures buried beneath a thin film was numerically simulated by using the Bethe-Bouwkamp model and the dependence of optical signal strength on subsurface depth was investigated [22]. On some specified samples, the permittivity and depth could be recovered from the measured near-field optical data [23]. However, in these prior investigations, the possible influence of buried structures’ geometry and dimension on near-field optical image contrast has not been fully explored. The maximum allowable cover thickness, i.e., the limit of subsurface depth for unambiguous optical sensing has not been quantitatively addressed. On the other hand, all such investigations are crucial toward understanding comprehensively the s-SNOM’s capability in imaging buried materials, inclusions and defects.
To elucidate the visibility of structures beneath a surface by s-SNOM, we designed and fabricated some reference samples, which were in a multilayered architecture. On the reference samples, we investigated the influence of geometry, dimension and coating thickness on near-field optical image contrast. Toward this main purpose, a gold film was deposited on a flat silicon substrate, and different patterned structures with precisely controlled shapes and dimensions were fabricated on the metal film. They were then covered with a polymethyl methacrylate (PMMA) layer having a predetermined thickness. The structures composed of either gold or silicon materials beneath the PMMA cover were the target characteristics in s-SNOM detection. The observed contrast was interpreted and discussed by using a simple dipole model.
2. Methods
2.1 Experimental setup
All the s-SNOM imaging experiments in this work were performed on a commercial system (NeaSNOM, Neaspec GmbH). The experimental setup is schematically illustrated in Fig. 1. An apertureless tip is coated with a platinum layer (ARROW NCPt, Nanoworld) and illuminated with a CW infrared laser at the wavelength of 10.663 µm. In the measurements, a beam splitter splits the laser path into two branches, namely the signal branch and the reference branch. The signal branch, which is laid out in the horizontal direction in Fig. 1(a), is focused onto the metallic probe tip by a parabolic mirror and the scattering light is reflected back to the beam splitter. The reference branch, which is laid out in the vertical direction in Fig. 1(a), is modulated by a vibration mirror and the mirror oscillates at a frequency K. The reflected light passes the same beam splitter and interferes with the signal beam. The interference light is fed into an infrared detector, which additionally couples the scattering from the sample surface and the probe shaft. To suppress background scattering, a pseudoheterodyne detection method is employed [24,25]. The probe vibrates at a frequency Ω and the scattering light containing the sample’s near-field properties is demodulated at frequencies nΩ+K and nΩ+2K with n the harmonic order. The harmonic amplitude and phase are simultaneously lock-in analyzed.
Fig. 1. (a) Schematic illustration of the experimental s-SNOM setup for investigating the visibility of buried structures in a multilayered architecture. The underneath structures are patterned on a metal film and they are covered with a thin polymer layer. A pseudoheterodyne detection method is employed to obtain background-free near-field optical signal. (b) Schematic illustration of the dipole model for a simple theoretical analysis.
The used samples were in a multilayer architecture. In preparation, a chromium film with a thickness of 5 nm was first deposited on a silicon substrate by using an electron-beam evaporator (LAB 18, Kurt J. Lesker) and a 50 nm thick gold film was subsequently deposited. Then, focused ion beam (FIB) was applied to etch the designed patterns on the evaporated gold film (NanoLab 650, FEI Helios). The circle and slit structures fabricated on the substrate were mainly concerned. The etching depth was the same of approximately 60 nm to ensure that the Cr/Au film was completely removed in the drilled area, leaving the silicon substrate as the top surface. An ion beam current of 40 pA and an acceleration voltage of 30 kV were optimized and used in FIB etching. The resulted structures are demonstrated in Fig. 2. The designed diameters of the circular patterns are respectively 1300, 1100, 900, 700, 500, 300 and 100 nm from the left to right columns as shown in Figs. 2(a) and 2(c). The slit widths are respectively 500, 450, 400, 350, 300, 250, 200, 150 and 100 nm and the lengths are the same of 4 µm as depicted partially in Figs. 2(b) and 2(d). The actual dimensions are in close accordance with the designed ones as verified in the experimental measurements and so we only present the design values here. The circular holes in the last column in the SEM image [see Fig. 2(c)] have a diameter smaller than 100 nm. These holes are neglected in the subsequent analysis because they are undetectable in s-SNOM imaging. After FIB processing, a 2 wt% PMMA solution was dropped and spin-coated. The spin speed was 6000 rpm and the sample was heated at 180 °C for 3 min to develop the PMMA film. The resulted thickness was approximately 50 nm as measured by an AFM (MFP-3D Origin, Asylum Research). Finally, repeating the coating procedure, a series of cover layer thicknesses could be obtained. In our s-SNOM imaging, it usually took about 25 min to scan a 10×10 µm image with 200×200 pixels.
Fig. 2. The patterned structures with controlled geometry and dimension by FIB processing. The sample before PMMA coating is a thin Au layer deposited on a Si substrate and the patterns are fabricated on the Au film. (a)(b) AFM and SEM images of the drilled circular holes with different diameters. (c)(d) AFM and SEM images of the slits with different widths. The scale bars in (c) and (d) are 2 µm.
2.2 Theoretical analysis based on a dipole model
For a simple analysis, a dipole model is utilized to calculate the intensity of scattering light as sketched in Fig. 1(b). The probe tip is approximated by a metallic sphere with radius R. Under the incident light field Ein, the tip polarizability is expressed as [26],
where ɛt is the dielectric constant of the tip. The dipole is polarized in the z-direction and the sample is polarized in turn when the tip apex is close enough to the sample surface. A mirror dipole is consequently created with the polarizability αβ where, In the above equation, β is the surface response function and ɛs is the dielectric constant of the sample. To describe the multiple interactions between tip and mirror dipoles, the effective polarizability is introduced, Here, z is the distance between tip and sample. Therefore, the intensity of the light measured at the detector is estimated as, where Es is the scattering field. The s-SNOM harmonic amplitude S and phase φ are evaluated by, The above model is suitable for analyzing the s-SNOM signals where the sample can be approximated as an infinite half-space. In this work, the sample structures with finite sizes are considered. The simplified theoretical analysis may have obvious discrepancies. However, the analyzed signal contrast between different materials remains reasonable and we prefer to use the above model for simplicity. Certainly, other more accurate approaches such as finite-difference time-domain (FDTD) computations based on experimental settings can be employed if necessary [27].3. Results and discussion
We first examined the structural visibility in the near-field optical image. The typical imaging results on the circular patterns are demonstrated in Fig. 3. In experiments, the probe was oscillated at a frequency of 264.5 kHz and the amplitude was approximately 30 nm. We recorded the third harmonic amplitude as the s-SNOM near-field optical image because it showed a better signal-to-noise ratio as compared with other harmonic orders and the signal strength was satisfactory. The signal-to-noise ratio was around 9 for the third harmonic signals and the subsurface materials could be unambiguously distinguished as shown in the following images. For other harmonics, for instance, the signal of the fourth harmonic was rather close to the noise level, which caused poor image contrast. When the PMMA cover is absent, the FIB drilled holes, even the ones with the diameter of 100 nm, can be clearly seen in the amplitude image as shown in Fig. 3(a). The minimum diameter of the sensible circular pattern increases if the PMMA coating thickness increases. For example, the holes in the sixth column with the diameter of 300 nm are resolved when the cover thickness is 50 nm but they fade out when the thickness increases up to 100 nm. Furthermore, the intensity of near-field optical signal decreases after covering the PMMA layer. The signal strength without covering [Fig. 3(a)] is almost 12 times of that with a 100 nm thick PMMA layer [Fig. 3(c)]. It is obvious that the cover thickness affects both the signal intensity and the contrast in detecting the beneath structure. In the acquired s-SNOM image, the signal difference between on the structure and on the substrate determines the visibility of the corresponding embedded feature. To evaluate the contrast quantitatively, we define the following metric,
where Sstr and Ssub are the third harmonic s-SNOM amplitudes on the patterned structure and on the surrounding substrate, respectively. In this work, a contrast threshold of larger than 0.05 is selected as the criterion for unambiguous discrimination of structural feature from the background signal. Figure 3(d) presents the evaluated modulation contrast of the patterns with different hole-diameters and cover thicknesses. The structures having the parameters fall in the shaded region are difficult to be observed. According to our criterion, the circular holes with the diameter of 300 nm are hardly distinguished and the rest larger patterns are obvious when the PMMA thickness is 100 nm. These predictions from the contrast threshold are in accordance with the near-field optical image shown in Fig. 3(c). When the PMMA layer becomes thinner, the minimum visible diameter decreases accordingly. It is approximately 121 nm if the cover thickness is only 50 nm. Therefore, the hole-structures with the diameter of 100 nm are almost invisible but the ones with the diameter of 300 nm are now distinguishable. These results again agree reasonably with the experimental s-SNOM image shown in Fig. 3(b). Besides the cover layer thickness, the structure dimension has significant influence on the optical contrast. When the diameter of the buried hole-structure increases, the contrast increases and then reaches a saturation, which is relevant with the PMMA cover thickness. Certainly, detecting a large structure is much easier. From the results, the saturated contrast is around 0.35 on the bare substrate and it is 0.22 and 0.13 when the coating thickness is 50 and 100 nm, respectively.Fig. 3. The third harmonic s-SNOM amplitude signals on the substrate patterned with circular hole-structures under different cover thicknesses. (a) Without the cover layer. (b) With the cover layer thickness of 50 nm. (c) With the cover layer thickness of 100 nm. (d) Amplitude modulation contrast M as a function of pattern diameter D. When the contrast is smaller than a threshold of 0.05 as illustrated in the shaded region, the corresponding structure is difficult to be distinguished. (e) Measured diameters of the circular hole-patterns from the s-SNOM images when the cover layer thickness is varied.
Along with the increase of cover thickness, the decrease of the minimum sensible diameter indicates that the apparent diameter in the optical image might decrease accordingly. Therefore, we measured the diameters of all the detectable circular patterns and compared with those from the SEM imaging as presented in Fig. 3(e). For the patterns without the coating layer, the measured diameters by SEM are the closest to the design values. Such results indicate that the accuracy of FIB milling is satisfactory and the discrepancy in the s-SNOM measurement is due to the limited image pixel density and subsequent an over-estimation of the diameter. When the cover thickness increases, the detected diameter from the near-field optical signal channel will decrease. Subsequently, the structures with the smallest diameter will disappear. In a short summary, the PMMA coating affects the s-SNOM amplitude strength and its contrast. Both of them decrease when the PMMA layer becomes much thicker. Besides material properties, the structural dimensions dominate the visibility of the subsurface structure in s-SNOM characterization. The smallest diameters of the fabricated structures that we can distinguish are around 100, 300 and 500 nm when the cover thicknesses are 0, 50 and 100 nm, respectively.
In addition to the circular patterns, we designed a sample containing a set of slits to explore the influence of structure geometry and coating thickness on the optical image contrast. Figure 4 presents the typical results. With the increase of PMMA thickness from 0 to 100 nm, the s-SNOM amplitude image contrast decreases. Among the different slit widths, the saturated contrast magnitudes are around 0.45, 0.18 and 0.13 when the cover thicknesses are 0, 50 and 100 nm, respectively. The general trend of the influence of PMMA coating on the detected s-SNOM amplitude is similar to that observed on the circular pattern. For the same threshold of contrast metric M, the width of the narrowest slit we can distinguish is smaller than 100 nm for both conditions where the PMMA coating thicknesses are 50 and 100 nm. The minimum width of the visible slit structure is smaller than the sensible diameter of the circular pattern as summarized in Table 1. Results indicate that the distinguishability of a buried structure in the s-SNOM image is also related to the geometry. The line-like structures are much easily detected as compared with the circle-like structures when the width and the diameter are equal and other experimental settings are kept the same.
Fig. 4. The third harmonic s-SNOM amplitude signals of the substrate drilled with slit patterns under different cover layer thicknesses. (a) Without the cover layer. (b) With the cover layer thickness of 50 nm. (c) With the cover layer thickness of 100 nm. (d) Amplitude modulation contrast M as a function of slit width W. When the contrast is smaller than a threshold of 0.05 as shown in the shaded region, the corresponding structure is difficult to be distinguished.
Table 1. Saturation contrast and the minimum detectable size.
We can find notable near-field enhancement of the light field around the pattern edges in Figs. 3 and 4, which is caused by the plasmonic field confined to the sharp edge of a metal structure. Such a phenomenon has been well understood in the past years [27]. The brighter rims are not perfectly symmetric in the s-SNOM images owing to the fabrication and coating imperfections. The strong field enhancement in the edge will affect the obtained image contrast when two structures are close to each other. If the gap is reduced, the narrowest slit may appear as a bright line and the smallest circular hole may look like a bright dot, leading to contrast reversal. Such an effect can be observed near the smallest structures.
From the above results, the visibility of circular-hole and slit is different even they have the same critical dimension. To address such an issue more intuitively, we fabricated a sample, in which the middle Au layer was drilled with dot and dash structures in form of Morse codes. We used the circular hole and the slit pattern to denote the dot and the dash in Morse coding. Both the dot diameter and the dash width are the same of approximately 100 nm and the dash length is 500 nm as presented in Fig. 5. From the SEM image and s-SNOM topography of the sample without PMMA coating, clear encoded information can be read out, which means “where there is a will, there is a way.”. However, after coating a thin PMMA layer with the thickness of approximately 70 nm, the dots fade out in the near-field optical image as demonstrated in Fig. 5(d). Only the dashes can be distinguished and the optical signal intensity of the dots is the same as that of the substrate, which is consistent with previous experimental results. Therefore, the encoded information on the patterns will be failed to read out. This experiment convincingly demonstrates that the structure shape and size together with the coating thickness play an important role in forming the subsurface material contrast. Such an observation is reasonable. We can consider the dash as a set of dots and the integration of the near-field signal of those dots will make the signal contrast of dash much stronger than that of a single dot. Though the critical dimensions of the structures are the same, their contrast in the s-SNOM image may be rather different.
Fig. 5. s-SNOM imaging of a sample with FIB processed structures in form of Morse coding. (a)(b)(c) SEM image, s-SNOM topography and the third harmonic s-SNOM amplitude of the sample without a coating layer. (d) s-SNOM amplitude image of the same substrate coated with a 70 nm thick PMMA layer.
To elucidate the contrast mechanism when measuring the patterned multilayer sample by s-SNOM, the dipole model as presented in Section 2.2 was utilized for theoretical calculation. The tip was approximated as a platinum sphere and its radius was 50 nm. The transmittance of the PMMA layer was larger than 0.9 in the calculated range of laser wavelength and so we approximated the thickness of PMMA coating as an air gap between tip apex and sample surface. The oscillation amplitude and frequency of the probe tip were respectively 30 nm and 264.5 kHz, in accordance with the experimental settings. The dielectric functions of the three materials namely gold, silicon and platinum were taken from those reported in literature [28–30]. It should be emphasized that the sample is considered as an infinite half-space for the analytical solutions and such an approximation deviates from the practical situations. We use such a simplified model to analyze the s-SNOM amplitude signal contrast between on gold and on silicon, and to explore the influence of tip-sample distance and the incident laser wavelength because the computed trends are reasonable. However, the effect of structure shape and size on the optical contrast requires further FDTD simulations.
For an incident laser wavelength from 8 to 12 µm, the third harmonic s-SNOM amplitudes on silicon and gold materials beneath a 50 nm thick PMMA capping layer are calculated as shown in the inset of Fig. 6(a). Here, the third harmonic amplitudes are normalized to the one on silicon at the incident laser wavelength of 8 µm. We can find that the amplitude on gold is larger than on silicon, in agreement with experimental observation. The s-SNOM signal contrast M is approximately 0.13 and it is almost constant within the wavelength range. The theoretical contrast is slightly smaller than the experimental saturation magnitudes of 0.22 and 0.18 for the circle and slit structures as presented in Table 1. The deviation is mainly caused by the model simplification. However, the orders of contrast magnitudes are in good agreement. We have also analyzed the influence of laser wavelength at a different range as shown in Fig. 6(c), where the contrast in the visible light band is provided. An evident peak at the wavelength of 520 nm emerges and the contrast metric M is around 0.34, which is much larger than that in the infrared domain. Results imply that selecting the incident laser in the visible especially at the wavelength near 520 nm can help to obtain stronger signal and better contrast. The influence of coating thickness on the contrast is presented in Fig. 6(b). In calculation, the distance between tip apex and sample surface is altered from 0 to 100 nm and the light wavelength is 10.663 µm. The contrast decays monotonously with the increase of PMMA thickness and it remains 0.13 when the tip-sample distance is 100 nm. According to the calculations, the detection depth (i.e., the allowable thickness of PMMA coating) can reach hundreds of nanometers, in agreement with the experimental results. However, a complete understanding of the subsurface structural visibility requires further detailed FDTD investigations. In addition to the above mentioned effect of structure geometry, size and cover thickness on the near-field optical contrast, it is affected by several other factors including the absorption of coating materials and stray light from the probe and sample. When the laser wavelength is changed to the visible range, the contrast M will become even larger. The contrast variation when the incident wavelength is 633 nm is illustrated in Fig. 6(d). A significant enhancement of contrast M can be obtained as compared with the infrared light. We can reasonably expect that the detectable depth under the visible light illumination could be much larger for these samples.
Fig. 6. Theoretical analysis of the third harmonic s-SNOM amplitude contrast. (a)(b) Dependence of the amplitude contrast M on the incident laser wavelength λ in the infrared region and the tip-sample gap z. The insets show the normalized amplitudes on the two different materials at the incident wavelength of 8 µm. (c)(d) Dependence of the amplitude contrast M on the incident wavelength λ in the visible light range and the tip-sample gap z. The wavelength is 10.663 µm in (b) and 633 nm in (d).
s-SNOM is sensitive to the change of sample’s dielectric constant and so the detection of small defects either on or under the surface is possible. As shown in above experiments, the near-field optical signals between on the substrate and on the patterned structures have satisfactory differences though the fabricated patterns are buried under a more than 100 nm thick PMMA layer. Consequently, we can expect the application of s-SNOM in non-invasive subsurface detection. However, for the above samples, the topography already has shallow features following the patterned structures beneath the surface though these features are blurred. To verify the subsurface imaging capability more directly, we fabricated nine cavities with a set of discrete diameters on a silicon substrate by FIB. After that, we covered the substrate with the adhesive glue of a bi-axially oriented polypropylene (BOPP) tape. The processed sample was then imaged by s-SNOM and the typical results were presented in Fig. 7. From the topography, the middle hole-structure is invisible because it is thoroughly covered by the BOPP tape materials. On the contrary, clear contrast of the buried cavity appears in the optical image as shown in Fig. 7(b) and its inset. The uncovered holes only have dark edges in the optical image and the near-field signal intensity of the rest part is the same as that on the substrate. This is owing to the fact that the dielectric constants of the substrate and the FIB drilled structure are both that of silicon. Note the sample here is without coating a gold film. However, the near-field signal intensity of the covered circular-hole is significantly weaker than that on the substrate and the contrast is induced by the dielectric difference between the filler in the drilled hole and the silicon. The sectional profiles of topography and s-SNOM amplitude image are compared in Fig. 7(c). From the topographic profile, the cover thickness is 60 nm and the depth of FIB drilling is 140 nm. In the optical profile, however, a drop with a lower signal strength is detected. The covered middle-hole is unmasked and such a feature is absent in the topography as guided by the shaded region. Results demonstrate that s-SNOM is capable of detecting embedded features in a non-destructive way and its sensible depth reaches a magnitude of around 200 nm. Therefore, it has great potential for applications in subsurface characterization as long as the buried defects, inclusions and objectives having enough optical differences as compared with their surrounding materials.
Fig. 7. Subsurface nano-imaging by s-SNOM. The sample is a patterned silicon substrate covered by the glue from a double-side tape. (a) Topography. (b) The third harmonic s-SNOM amplitude. The inset is a zoomed view of the area sketched by the dashed rectangle. (c) Sectional profiles of the topography and amplitude images. The two profiles are taken from the same position as guided by the dashed line in topography.
4. Conclusions
The factors affecting subsurface material contrast and structural visibility via s-SNOM were investigated systematically. A type of multilayered samples composed of a silicon substrate, a patterned gold film and a PMMA cover were employed for s-SNOM imaging. The patterned gold structures were circular holes and slits having precisely controlled sizes. The influences of geometry, dimension and cover thickness on s-SNOM amplitude contrast between the patterned area and the surrounding medium were considered in detail. The contrast was reasonably interpreted by using a simple dipole model. Our experiments demonstrate that under the same experimental settings, the slit is easier to be distinguished than the circular hole with the same critical dimensions. The signal contrast decays along with the increase of cover thickness. The s-SNOM method can sense the material contrast between gold and silicon under the PMMA layer with the thickness of larger than 100 nm and the subsurface resolution is better than 100 nm. The above studies elucidate the capability and potential application of s-SNOM in subsurface imaging and defect inspection at the nanometer scale resolution.
Funding
National Natural Science Foundation of China (51675504).
Acknowledgments
We acknowledge for the support of this work by allocating us resources of the USTC Center for Micro- and Nanoscale Research and Fabrication.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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